Could one run a nozzle check once a week or so to pump a bit of ink through?

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In short, yes, of course you can do that.
I have "saved" an inkjet test page (there are lots of these on the net) to my iPad, and email it to my printer every week. My printer is Epson L805, and it is wifi! I do it from my iPad at home, and from wherever I am when I am away. If your printer is not wifi, you can print the test page directly from your computer as well. I am away for several months in the year, and up to now, my printer has not clogged, unlike many previous Epsons (which didn't have wifi).
I hope this is helpful to you.